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avatar+893 

Can anyone solve this? (without calculator please) Answer: 0.25

 Mar 14, 2019
edited by dgfgrafgdfge111  Mar 15, 2019
 #1
avatar+893 
0

Here's what I tried:

 

First I looked at 1.75 + sqrt(3) and said, "Well, why not set it equal to a variable?". So I replaced it with x.

 

Then I got \(2\sqrt{x} - x\), but that didn't help at all. I can't set it equal to anything. I can't solve it with a variable. So then I thought I would just need to solve it by hand. But how in the world would I know what \(\sqrt{3}\) was? Luckily, I remebered that it was 1.732. So, thenI solved it as shown below:

 

\(2\sqrt{1.75+1.732} - (1.75+1.732)\)

 

\(=2\sqrt{3.482}-3.482\)

 

Now what? How do I solve this?

 Mar 15, 2019
 #3
avatar+4322 
+2

Try to square it. Do you think approximations would help? 

tertre  Mar 15, 2019
 #5
avatar+893 
0

If we squared it, though, we would get 2(sqrt(3.482)), which wouldn't simplify.

dgfgrafgdfge111  Mar 15, 2019
 #6
avatar+4322 
+2

It actually gets around 0.2500002, so 0.25.

tertre  Mar 15, 2019
 #7
avatar+893 
0

Did you use calc or use approximates?

dgfgrafgdfge111  Mar 15, 2019
 #2
avatar+103674 
0

\(2\sqrt{1.75+\sqrt3}-(1.75+\sqrt3)\\ \)

 

I'm coming up blank.

but   sqrt root of 3   is irrational so it is not exactly equal to what you said.  

 Mar 15, 2019
 #4
avatar+893 
0

Yeah, I just approximated it.

dgfgrafgdfge111  Mar 15, 2019
 #8
avatar+103674 
+2

Finally I got it !!

 

\(2\sqrt{1.75+\sqrt3}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{4(\frac{7}{4}+\sqrt3)}\qquad -(1.75+\sqrt3)\\~\\ =\sqrt{7+4\sqrt3}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{(2)^2+(2*2*\sqrt3)+(\sqrt3)^2}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{(2+\sqrt3)^2}\qquad-(1.75+\sqrt3)\\~\\ =(2+\sqrt3)\qquad-(1.75+\sqrt3)\\~\\ =2+\sqrt3-1.75-\sqrt3\\~\\ =0.25\)

 

Is that impressive or what!   LOL

 Mar 15, 2019
 #9
avatar+893 
+1

Wow, that's smart!!!!

dgfgrafgdfge111  Mar 15, 2019

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